Generalized Kittel-Van Vleck Relation betweengandg′; Validity for NegativegFactors

It is pointed out that a generalized exact relationship exists between the spectroscopic splitting factor $g$ and the magnetomechanical ratio $g^{\prime }$ for paramagnetic centers: $g^{\prime }=\frac{g}{(g-\rho )}$ with $\rho =\frac{〈S_z〉}{{S_z}^{\prime }}$. Here $S^{\prime }$ is the fictitious spin in the spin Hamiltonian and $〈S_z〉$ is the expectation value of the real spin in the state labeled by ${S_z}^{\prime }$; the $z$ axis is defined by the direction of magnetic field. Several classes of magnetic systems are considered, where for each system $\rho$ is constant over a wide range of physical parameters such as cubic crystal field and spin-orbit coupling, expressing an underlying symmetry of the magnetic ion in its environment. It is shown that the sole criterion for validity of the Kittel-Van Vleck relation $g^{\prime }=\frac{g}{\mathrm{}(g-1\mathrm{})\mathrm{}}$ is that $〈S_z〉={S_z}^{\prime }$ and that this may occur even when the admixed orbital angular momentum is very large so that the departure of $g$ from 2 is very large. The generalized relation between $g$ and $g^{\prime }$ is also applied to cases where $g$ is negative while $g^{\prime }$ is positive. The extension of the relation between $g$ and $g^{\prime }$ to cases of interacting magnetic centers is discussed.